Simulations - PhysLab

First Pendulum Angle: 45°

Second Pendulum Angle: 22.5°

First Pendulum Length: 80

Second Pendulum Length: 80

First Bob Mass: 10

Second Bob Mass: 10

Gravity: 1.0

Damping: 0.999

About Double Pendulum Chaos

The double pendulum is a classic example of chaotic motion in physics. It consists of one pendulum attached to another, creating a system that is extremely sensitive to initial conditions.

The equations governing double pendulum motion are derived from Lagrangian mechanics and can't be solved analytically.

This system demonstrates the "butterfly effect" - tiny changes in initial position lead to completely different trajectories over time.

Watch the pink trail to visualize the path of the second bob over time, demonstrating the unpredictable nature of chaotic systems.

About Electric Field Visualization

This simulation demonstrates the electric field created by point charges in space. The field lines show the direction a positive test charge would move if placed in the field.

Coulomb's Law: F = k(q₁q₂/r²)

Electric Field: E = F/q = k(q/r²)

Drag charges to reposition them. Double-click on a charge to remove it. Positive charges (red) create field lines that emanate outward, while negative charges (blue) have field lines pointing inward.

Potential Type

Initial Wave Packet

About Quantum Wave Function

This simulation visualizes the time evolution of a quantum wave function in one dimension, demonstrating fundamental quantum mechanical principles.

Schrödinger Equation: iħ∂ψ/∂t = -ħ²/2m ∂²ψ/∂x² + V(x)ψ

Probability Density: P(x) = |ψ(x)|²

The blue line represents the real part of the wave function, while the pink area below shows the probability density. Watch how the wave packet interacts with different potential energy configurations.

Object Shape

About Fluid Dynamics

This simulation demonstrates fluid flow around obstacles, visualizing concepts like turbulence, vortex shedding, and Bernoulli's principle.

Navier-Stokes Equations (simplified): ∂v/∂t + (v·∇)v = -∇p/ρ + ν∇²v

Bernoulli's Equation: p + ½ρv² + ρgh = constant

Move your mouse through the fluid to interact with the flow. Change the obstacle shape to see how different objects affect the fluid dynamics.

Source 1 Frequency: 5

Low High

Source 2 Frequency: 5

Low High

Amplitude: 10

Small Large

About Wave Interference

When two or more waves meet, they interact through the principle of superposition, creating patterns of constructive and destructive interference.

Wave equation: y(x,t) = A sin(kx - ωt + φ)

For superposition: y_total = y₁ + y₂

Adjust the frequency and amplitude of both sources to observe how the interference pattern changes.

Mass 1

Light Heavy

Mass 2

Light Heavy

Initial Velocity

Slow Fast

About Elastic Collisions

In an elastic collision, both momentum and kinetic energy are conserved. This simulation demonstrates how objects of different masses interact during collisions.

Conservation of Momentum: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Conservation of Kinetic Energy: ½m₁v₁² + ½m₂v₂² = ½m₁v₁'² + ½m₂v₂'²